From the experimental perspective, the obtained systems from our \(q\) th-rooting procedure are expected to be implementable with the same setups employed for realizing their parent models. To this end, the additional degrees of freedom required in our \(q\) th-rooting procedure can be principally implemented by coupling multiple copies of the target system. In the context of the non-Hermitian FTIs and FSOTIs explored in this paper, their corresponding square- and cubic-root systems can thus be realized in principle via setups like photonic quantum walks [1]}, [2]}, [3]}, [4]}, [5]}. For example, the anisotropic hopping amplitude and non-Hermitian lattice potential in our parent models can be implemented by introducing controlled optical losses with acousto-optical modulators in coupled optical fibre loops [1]}. Moreover, the winding number invariants used in characterizing their topology can in principle be experimentally probed via measuring mean chiral displacements [7]}, [8]}, [9]} or time-averaged spin textures [10]}, [11]}, which can also be conducted in similar photonic setups [2]}, [3]}, [4]}, [5]}.
